Question

The goal of this question is to practice the application of statistics to do a quantitative genetics study of a population. Use the following data on the phenotype (P) of the variables: days to reach 230 lb (denoted D, day units) and backfat thickness (denoted B, inch units) in pigs. All answers must be computed manually and this work must be shown. Optionally, you can confirm your manual calculations using Excel or similar software or functions. Show your workand steps to obtain all your answers.

Pig number      Days to 230 lb, days      Backfat thickness, inches

1                      164                                1.1

2                      181                                1.2

3                      168                                1.6

4                      170                                1.8

5                      198                                1.3                 

1.1) [10 points] Provide the estimates of correlation between P and B (), regression of D on B (), and regression of B on D (). Show your work to compute the means, variances, standard deviations, and covariances necessary to obtain the correlation and regression estimates. Include unitswith your answers. Round your answers to the thousandths (third decimal place).

• Provide
• Provide  and interpret this regression estimate in your own words (for example, D increases 5.5 units per unit increase in B)
• Provide  and interpret this regression estimate in your own words

Answer:

1.2) [10 points] Provide the predicted value for B of a new pig that has a D = 190 days based on the values computed in question 1.1). Show your work and round your answer to the thousandths (third decimal place). Include unitswith your answer.

Please show work!

Answer 1

Pig(P)	D	B
1.000	164.000	1.100
2.000	181.000	1.200
3.000	168.000	1.600
4.000	170.000	1.800
5.000	198.000	1.300
mean(D)	mean(B)	mean(P)	sB	sD
176.200	1.400	3.000	0.261	12.270
correlation coefficient:		r(P,D)=	0.657	r(D,B)=	-0.225		b(B,D)=	-0.005
							b(D,B)=	-10.588
Regression of B on D:
B = mean(B) + b(B,D)(D-mean(D))
B = 1.4 + (-0.005)(D-176.2)
B = 2.281 - 0.005D
Regression of D on B:
D = 176.2 - 10.588(B - 1.4)
D = 191.023 - 10.588B

From both regression equations, B decreases as D increases or D decreases as B increases.

Now, D = 190 implies predicted value of B = 1.331.